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Cover Art
Author Farkov, Yu. A., author.

Title Construction of wavelets through Walsh functions / Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi.

Published Singapore : Springer, [2019]


Location Call No. Status
Physical description 1 online resource
Series Industrial and applied mathematics
Industrial and applied mathematics.
Springer Mathematics and Statistics eBooks 2019 English+International
Bibliography Includes bibliographical references and index.
Contents Intro; Preface; References; Contents; About the Authors; Introduction; References; 1 Introduction to Walsh Analysis and Wavelets; 1.1 Walsh Functions; 1.2 Walsh-Fourier Transform; 1.3 Haar Functions and Its Relationship with Walsh Functions; 1.4 Walsh-Type Wavelet Packets; 1.5 Wavelet Analysis; 1.5.1 Continuous Wavelet Transform; 1.5.2 Discrete Wavelet System; 1.5.3 Multiresolution Analysis; 1.6 Wavelets with Compact Support; 1.7 Exercises; References; 2 Walsh-Fourier Series; 2.1 Walsh-Fourier Coefficients; 2.1.1 Estimation of Walsh-Fourier Coefficients
2.1.2 Transformation of Walsh-Fourier Coefficients2.2 Convergence of Walsh-Fourier Series; 2.2.1 Summability in Homogeneous Banach Spaces; 2.3 Approximation by Transforms of Walsh-Fourier Series; 2.3.1 Approximation by Césaro Means of Walsh-Fourier Series; 2.3.2 Approximation by Nörlund Means of Walsh-Fourier Series in Lp Spaces; 2.3.3 Approximation by Nörlund Means in Dyadic Homogeneous Banach Spaces and Hardy Spaces; 2.4 Applications to Signal and Image Processing; 2.4.1 Image Representation and Transmission; 2.4.2 Data Compression; 2.4.3 Quantization of Walsh Coefficients
2.4.4 Signal Processing2.4.5 ECG Analysis; 2.4.6 EEG Analysis; 2.4.7 Speech Processing; 2.4.8 Pattern Recognition; 2.5 Exercises; References; 3 Haar-Fourier Analysis; 3.1 Haar System and Its Generalization; 3.2 Haar Fourier Series; 3.3 Haar System as Basis in Function Spaces; 3.4 Non-uniform Haar Wavelets; 3.5 Generalized Haar Wavelets and Frames; 3.6 Applications of Haar Wavelets; 3.6.1 Applications to Solutions of Initial and Boundary Value Problems; 3.6.2 Applications to Solutions of Integral Equations; 3.7 Exercises; References
4 Construction of Dyadic Wavelets and Frames Through Walsh Functions4.1 Preliminary; 4.2 Orthogonal Wavelets and MRA in L2(mathbbR+); 4.3 Orthogonal Wavelets with Compact Support on mathbbR+; 4.4 Estimates of the Smoothness of the Scaling Functions; 4.5 Approximation Properties of Dyadic Wavelets; 4.6 Exercise; References; 5 Orthogonal and Periodic Wavelets on Vilenkin Groups; 5.1 Multiresolution Analysis on Vilenkin Groups; 5.2 Compactly Supported Orthogonal p-Wavelets; 5.3 Periodic Wavelets on Vilenkin Groups; 5.4 Periodic Wavelets Related to the Vilenkin-Christenson Transform
5.5 Application to the Coding of Fractal FunctionsReferences; 6 Haar-Vilenkin Wavelet; 6.1 Introduction; 6.2 Haar-Vilenkin Wavelets; 6.2.1 Haar-Vilenkin Mother Wavelet; 6.3 Approximation by Haar-Vilenkin Wavelets; 6.4 Covergence Theorems; 6.5 Haar-Vilenkin Coefficients; 6.6 Exercises; References; 7 Construction Biorthogonal Wavelets and Frames; 7.1 Biorthogonal Wavelets on R+; 7.2 Biorthogonal Wavelets on Vilenkin Groups; 7.3 Construction of Biorthogonal Wavelets on The Vilenkin Group; 7.4 Frames on Vilenkin Group; 7.5 Application to Image Processing; References
Notes 8 Wavelets Associated with Nonuniform Multiresolution Analysis on Positive Half Line
Other author Manchanda, P. (Pammy), author.
Siddiqi, A. H., author.
SpringerLink issuing body.
Subject Wavelets (Mathematics)
Walsh functions.
Electronic books.
Electronic books.
ISBN 9789811363702 electronic book
9811363706 electronic book